Threshold law for ionization cross sections in the Temkin-Poet model

An integral representation of wave functions for the Temkin-Poet model of electron impact on atomic hydrogen is given. Approximate wave functions are evaluated analytically for large hyperradius to extract the ionization S-matrix element. An ionization cross section of the form exp[-${\mathrm{aE}}^{\mathrm{-}1\mathrm{/}6}$+${\mathrm{bE}}^{1\mathrm{/}6}$], where a and b are positive constants, is derived. The exponential suppression of ionization for small E appears to be the quantum counterpart of the delayed onset of ionization in the classical theory for this model.